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Scale analysis for water jet impingement over a horizontal flat plate under film boiling configuration

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Abstract

A scale analysis has been performed to investigate the film boiling heat transfer associated with cooling of a horizontal flat plate through water jet impinging. The forced convection film boiling of water is treated by classifying a wide spectrum of subcooling regime by two extreme situations of low and high subcooling dominated by mass evaporation and sensible heating respectively. A simple expression of heat ratio is derived for executing the classification. The ratio is derived by considering the heat and mass transport phenomena and vaporization effect. The radiation heat effect is considered, while obtaining the scale of wall Nusselt number for convective and total heat transfer under both low and high subcooling cases. The comparison of the developed correlations, based on scaling, are made for the wall superheat between 290 and 1100 °C and jet velocity of water between 0.4–3.2 m/s along with the variation of water subcooling between 5 and 45 °C. The proper coefficient of the scaling is developed by making overall comparison of the data from the analysis with experimental data to predict the heat transfer. The effect of liquid to vapor viscosity ratio indicates a substantially higher Nusselt number for the jet impingement of plate under film boiling condition. The density ratio influences the heat transfer only at low subcooling condition. A lower Jakob superheat number, higher Jakob liquid subcooling number, and higher jet Reynolds number increases Nusselt number.

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Abbreviations

d :

Jet diameter

g :

Gravitational acceleration

Gr l :

Liquid phase Grashoff number \( =g{\beta}_l\left({T}_{sat}-{T}_{\infty}\right){L}_{\lambda}^3/\left({\nu}_l^2\right) \)

Nu R :

Convective heat transfer co-efficient

h fg :

Latent heat of vaporization

Ja sub :

Jakob number associated with subcooling of water =cpl(Tsat − T∞)/hfg

Ja sup :

Jakob number associated with superheating of vapor =cpv(Tw − Tsat)/hfg

j :

Mass flux

k :

Thermal conductivity

p :

Pressure

Prl :

Water Prandtl number

Prv :

Vapor Prandtl number

Ra l :

Water Rayleigh number \( =g{\beta}_l\left({T}_{sat}-{T}_{\infty}\right){L}_{\lambda}^3/\left({\nu}_l{\alpha}_l\right) \)

Rel :

Water Reynolds number =(u∞Lλ)/νl

Rev :

Vapor Reynolds number =(u∞Lλ)/νv

T :

Temperature

u, v :

Components of velocity

r, θ, z :

Coordinates

α :

Thermal diffusivity

β :

Volumetric thermal expansion co-efficient

δ :

Film thickness of vapor

δ l :

Thickness of liquid momentum boundary layer

δ t :

Thickness of liquid thermal boundary layer

ε :

Surface emissivity

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

σ :

Stefan–Boltzmann constant for radiation heat transfer

σ t :

Surface tension of water

0:

Jet initial position at the nozzle exit

eq :

Equivalent

hs:

High subcooling

ls:

Low subcooling

i :

Interface

l :

Water Phase

r :

Radiation heat transfer

sat :

Saturation value

v :

Vapor phase

w :

Plate surface

∞:

Free stream zone

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Acknowledgements

The authors express their gratitude towards Dr. Pallab Sinha Mahapatra, Assistant Professor, Department of Mechanical Engineering, IIT Madras for his valuable suggestions to enhance the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mechanical Engineering, NIT Agartala, Agartala, 799046, India

    Dipak Chandra Das

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Koushik Ghosh & Dipankar Sanyal

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  1. Dipak Chandra Das
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  2. Koushik Ghosh
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Correspondence to Dipak Chandra Das.

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Das, D.C., Ghosh, K. & Sanyal, D. Scale analysis for water jet impingement over a horizontal flat plate under film boiling configuration. Heat Mass Transfer 57, 1211–1221 (2021). https://doi.org/10.1007/s00231-021-03024-x

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